TY - JOUR
T1 - On the variance of single-run unbiased stochastic derivative estimators
AU - Cui, Zhenyu
AU - Fu, Michael C.
AU - Hu, Jian Qiang
AU - Liu, Yanchu
AU - Peng, Yijie
AU - Zhu, Lingjiong
N1 - Publisher Copyright:
Copyright © 2019 Informs.
PY - 2020/3
Y1 - 2020/3
N2 - We analyze the variance of single-run unbiased stochastic derivative estimators. The distribution of a specific conditional expectation characterizes an intrinsic distributional property of the derivative estimators in a given class, which, in turn, separates two of the most popular single-run unbiased derivative estimators, infinitesimal perturbation analysis and the likelihood ratio method, into disjoint classes. In addition, a necessary and sufficient condition for the estimators to achieve the lowest variance in a certain class is provided, as well as insights into finding an estimator with lower variance. We offer a sufficient condition to substantiate the rule of thumb that the infinitesimal perturbation analysis estimator has a smaller variance than does the likelihood ratio method estimator and to provide a counterexample when the sufficient condition is not satisfied.
AB - We analyze the variance of single-run unbiased stochastic derivative estimators. The distribution of a specific conditional expectation characterizes an intrinsic distributional property of the derivative estimators in a given class, which, in turn, separates two of the most popular single-run unbiased derivative estimators, infinitesimal perturbation analysis and the likelihood ratio method, into disjoint classes. In addition, a necessary and sufficient condition for the estimators to achieve the lowest variance in a certain class is provided, as well as insights into finding an estimator with lower variance. We offer a sufficient condition to substantiate the rule of thumb that the infinitesimal perturbation analysis estimator has a smaller variance than does the likelihood ratio method estimator and to provide a counterexample when the sufficient condition is not satisfied.
KW - Infinitesimal perturbation analysis
KW - Likelihood ratio method
KW - Simulation
KW - Stochastic derivative estimation
KW - Variance
UR - http://www.scopus.com/inward/record.url?scp=85089417624&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85089417624&partnerID=8YFLogxK
U2 - 10.1287/ijoc.2019.0897
DO - 10.1287/ijoc.2019.0897
M3 - Article
AN - SCOPUS:85089417624
SN - 1091-9856
VL - 32
SP - 390
EP - 407
JO - INFORMS Journal on Computing
JF - INFORMS Journal on Computing
IS - 2
ER -